Question

the ratio of masses of two planets is 2:3 and the ratio of thier radii is 4:7. Find the ratio of their acceleration due to gravity​

Answer 1

The ratio of their acceleration due to gravity​ is 49/24

Explanation:

We know that the gravitational force  is equal to

g1 = GM1/R^2

g2  =GM 2/R^2

Ratio of acceleration due to gravity.

g1/g2 =(M1/R1^2)/(M2/R2^2)

By substituting the values , it gives

g1/g2 = 2/(4)^2 /3 / (7)^2

g1/g2 = 49/24

Thus the ratio of their acceleration due to gravity​ is 49/24.

Also learn more

What is momentum ?

https://brainly.in/question/1535814

Answer 2

• The ratio of acceleration due to gravity is $\sf{\dfrac{g_1}{g_2}}\:=\:{\dfrac{49}{24}}$

Explanation:

Given :

• The Ratio of masses of two planets, $\sf{m_1\:{:}\:m2}$ = $\sf{2\:{:}\:3}$
• The Ratio of radii of two planets, $\sf{R_1\:{:}\:R_2}$ = $\sf{4\:{:}\:7}$

We know that,

$⟹ \sf{g\:=\:{\dfrac{GM}{R²}}}$

$⟹ \sf{\dfrac{g_1}{g_2}\:=\:{\dfrac{\dfrac{GM_1}{R_1^2}}{\dfrac{GM_2}{R_2^2}}}}$

$⟹ \sf{\dfrac{{\cancel{G}}M_1}{R_1^2}}\:×\:{\dfrac{R_2^2}{{\cancel{G}}M_2}}$

$⟹ \sf{\dfrac{M_1}{M_2}}\:×\:{\dfrac{R_2^2}{R_1^2}}$

$⟹ \sf{\dfrac{2}{3}}\:×\:{\dfrac{7²}{4²}}$

$⟹ \sf{\dfrac{{\cancel{2}}\:×\:49}{3\:×\:{\cancel{16}}}}$

$⟹ \sf{\dfrac{g_1}{g_2}}\:=\:{\dfrac{49}{24}}$

• Hence, the ratio acceleration due to gravity is $\sf{\dfrac{g_1}{g_2}}\:=\:{\dfrac{49}{24}}$